The present invention relates to an LSP prediction coding method and apparatus and, more particularly, to a line spectrum pair (LSP) prediction coder used for speech coding and a decoding system.
Medium and low bit rate and high efficiency speech signal coding have been generally executed by separating a linear filter representing spectrum envelope components and an excitation signal based on linear prediction analysis of speech. A typical method in the art is CELP (Code Excited Linear Prediction). For the CELP, M. Schroeder, "Code Excited linear prediction: High Quality Speech at very low bit rate", Proc. ICASSP, pp. 937-940 1985 (hereinafter referred to as Literature 1) may be referred to.
In the CELP, a speech signal is divided into blocks (or frames) of a short time period (for instance 10 msec.) for frame-by-frame coding. In the coding of linear prediction coefficients representing spectrum envelope components, the linear prediction coefficients are converted into line spectrum pairs (LSP). For conversion of line spectrum coefficient into LSP, Sugamura et al, "Speech Data Compression by Line Spectrum Pair (LSP) Speech Analysis Synthesis Process", Transactions of IECE of Japan A, J64-A, NO. 8, pp. 599-606, 1981 (hereinafter referred to as Literature 2) may be referred to.
In the prior art LSP prediction coders, efficient coding utilizing LSP inter-frame correlation is realized by making linear prediction of input LSP (or input vector) of the present frame by using quantizer output (i.e., codevectors) of past frames and quantizing the difference between the predicted vector obtained by the prediction and the input vector. For LSP prediction coders, Ohmuro et al, "Vector Quantization of LSP Parameters using moving means inter-frame prediction", Transactions of IECE of Japan, J77-A, No. 3, pp. 303-312, 1994 (hereinafter referred to as Literature 3) may be referred to.
Prediction coder output vector q(n) of n-th frame is given as: ##EQU1## where c(n) is n-th frame codevector supplied from the quantizer, x.sup.- (n) is n-th frame predicted vector, A.sub.i (n) (i=1, . . . ,M) is the n-th frame prediction coefficient matrix, and M is the degree of prediction. The symbol ".sup.- " in x.sup.- (n) is formally provided atop x in the formulas, but in the specification it is expressed as in x.sup.-.
Denoting the degree of LSP by P, q(n), c(n) and x.sup.- (n) are P-th degree vectors, and A.sub.i (n) is a (P.times.P) matrix.
The prediction coefficient matrix A.sub.i (n) (i=1, . . . ,M) is obtained in advance in a manner as will be described hereinunder such that predicted error energy E given by following formula (3) is minimized. ##EQU2## where x(n) is the n-th frame input vector, and EQU {n; x(n).epsilon..OMEGA.}
is aggregation of frames, in which the input vector x(n) is contained in aggregation .OMEGA.. The aggregation .OMEGA. is a vector aggregation obtained from a number of speech signals.
A.sub.i (n) (i=1, . . . ,M) is expressed as: ##EQU3## and (P.multidot.P.multidot.M)-th degree vector .lambda. defined as the following formula (5) by using elements a.sub.i,jk (i=1, . . . ,M, j, k=1, . . . ,P). EQU .lambda.=[a.sub.1,11, . . . , a.sub.1,1P, . . . , a.sub.1,P1, . . . , a.sub.1,PP, . . . , a.sub.M,11, . . . , a.sub.M,1P, . . . , a.sub.M,P1, . . . , a.sub.M,PP ].sup.T (5)
(P.multidot.P.multidot.M).times.P matrix V(n) is defined by formula (6). EQU V(n)=[F.sub.1 (n)F.sub.2 (n) . . . F.sub.M (n)] (6)
where (P.multidot.P).times.P submatrix F.sub.i (n) (i=1, . . . ,M) is expressed by the following formula (7) by using elements c.sub.j (n) of the codevector c(n). ##EQU4##
The n-th frame prediction vector x.sup.- (n) is expressed by the following formula (8) by using the matrix V(n) and vector .lambda.. ##EQU5##
The predicted error energy E given by the formula (3) thus can be expressed by the following formula (9). ##EQU6##
Since the partial differentiation of the predicted error energy E with respect to .lambda. is zero, EQU .differential.E/.differential..lambda.=0
simultaneous linear equations given by the following formulas (10) can be obtained. ##EQU7##
By solving the equations (10) for the vector .lambda., it is possible to obtain prediction coefficient matrix A.sub.i (i=1, . . . ,M) which minimizes the predicted error energy E given by the formula (3) from the relations of the above formulas (4) and (5).
It is also possible to obtain performance improvement by switching the prediction coefficient matrix A.sub.i (i=1, . . . ,M) in dependence on the character of the input speech signal.
A prior art LSP prediction coder will now be described with reference to FIG. 7. The Figure is a block diagram showing the prior art LSP prediction coder.
Referring to the FIG. 7, the n-th frame input vector x(n) is supplied from an input terminal 10. A memory 113 receives and accumulates codevector c(n) supplied from a quantizer 110.
A predictor 111 receives codevectors c(n-i), (i=1, . . . ,M) for past M frames and prediction coefficient matrix A.sub.i (n) (i=1, . . . ,M) which has been obtained in the manner as described above and stored in a prediction coefficient codebook 112, and calculates and provides predicted vector x (n) given by the formula (2).
A subtracter 120 receives the input vector x(n) and the predicted vector x.sup.- (n), and provides difference vector e(n)=x(n)-x.sup.- (n) representing the difference between the input vector x(n) and the predicted vector x.sup.- (n).
The quantizer 110 receives and quantizes difference vector e(n), and thus obtains and provides codevector c(n). The quantization may be performed by the vector quantization. For LSP vector quantization, K, Paliwal et al, "Efficient Vector Quantization of LSP Parameters at 24 Bits/Frame", IEEE transactions on Speech and Audio Processing, Vol. 1, No. 1, January 1993 (hereinafter referred to as Literature 4) may be referred to.
An adder 130 receives the codevector c(n) and the predicted vector x.sup.- (n), and obtains and provides output vector q(n) by adding together the codevector c(n) and the predicted vector x.sup.- (n) to an output terminal 11.
The above prior art prediction coder concerns moving mean prediction. Autoregressive prediction may be realized by substituting the following formula (11) for the formula (2). ##EQU8##
The LSP prediction coder as described above, has a problem that the prediction performance may be unsatisfactory depending on input LSP (i.e., input vector) supplied thereto.
This is because the prediction is performed for infinite kinds of input vectors that exist by using a prediction coefficient matrix obtained in advance.